Name: Solving Free Fall Problem Using Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 7 s
Description: In this video, we will learn how we can solve the problem of free fall effectively using the quadratic equation. Let's watch the video and learn.

Question

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for

4

hours and the pipe of smaller diameter for

9

hours, only half of pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of the smaller diameter takes

10

hours more than the pipe of larger diameter to fill the pool?

Accepted Answer

Let the time taken by larger diameter pipe to fill the pool be $x$ hours.

The smaller diameter takes $10$ hours more than the pipe of larger diameter to fill the pool

Therefore, the time taken by smaller diameter pipe to fill the pool $= (x + 10)$ hours

Part of the pool filled by larger diameter pipe in $1$ hour $= \frac{1}{x}$

Part of the pool filled by smaller diameter pipe in $1$ hour $= \frac{1}{x + 10}$

Given, when the larger diameter pipe is used for $4$ hours and the smaller diameter pipe is used for $9$ hours, then half the pool can be filled.

Therefore, $\frac{4}{x} + \frac{9}{x + 10} = \frac{1}{2}$

$\Rightarrow \frac{4 (x + 10) + 9 x}{x (x + 10)} = \frac{1}{2}$

$\Rightarrow \frac{13 x + 40}{x^{2} + 10 x} = \frac{1}{2}$

$\Rightarrow x^{2} + 10 x = 26 x + 80$

$\Rightarrow x^{2} - 16 x - 80 = 0$

$\Rightarrow x^{2} - 20 x + 4 x - 80 = 0$ (Splitting the middle term)

$\Rightarrow x (x - 20) + 4 (x - 20) = 0$

$\Rightarrow (x + 4) (x - 20) = 0$

$\Rightarrow (x + 4) = 0$ , $(x - 20) = 0$

$\Rightarrow x = - 4$ or $x = 20$

Thus, $x = 20$ ( $∵$ Time cannot be a negative integer)

Then, $x + 10 = 20 + 10 = 30$ hours

Hence, time taken by larger diameter pipe to fill pool separately is $20$ hours and time taken by smaller diameter pipe to fill pool separately is $30$ hours

Important Questions on Quadratic Equations

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